Automorphisms of partition order-decreasing transformation monoids

作者：Yang, Haobo; Yang, Xiuliang^*

来源：Semigroup Forum, 2012, 85(3): 513-524.

DOI：10.1007/s00233-012-9430-2

• Transformation semigroup
• Partition order-decreasing
• Automorphism group

Let T (n) be the full transformation semigroup on a finite set X (n) ={1,2,aEuro broken vertical bar,n}. Let rho be an equivalence relation on X (n) and a(a)- be a total order on the partition set X (n) /rho. We describe all automorphisms of the partition order-decreasing transformation monoid:
T (rho, <=) = {alpha is an element of T-n : (x alpha)rho <= x rho,. for all x is an element of X-n}
that generalizes the results of Schreier (Fundam. Math., 28:261-264, 1936) and utov (Izv. Vys. Uebn. Zaved., Mat., 3:177-184, 1961).

• 出版日期2012-12
• 单位杭州师范大学